Paper available: Modelling Collective Excitations in Cortical Tissue

[Werner Kistler]

The following paper is available on my web page:

http://www.physik.tu-muenchen.de/~wkistler/kistler98a.html

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W. M. Kistler, R. Seitz, and J. L. van Hemmen.
Modelling Collective Excitations in Cortical Tissue.
Physica D, 114(3/4): 273-295, 1998.

Abstract: 

We study a two-dimensional system of spiking neurons with local
interactions depending on distance. The interactions between the neurons
decrease as the distance between them increases and can be either
excitatory or inhibitory. Depending on the mix of excitation and
inhibition, this kind of system exhibits a rich repertoire of collective
excitations such as traveling waves, expanding rings, and rotating
spirals.  We present a continuum approximation that allows an analytic
treatment of plane waves and circular rings. We calculate the dispersion
relation for plane waves and perform a linear stability analysis.  Only
waves that have a speed of propagation below a certain critical
velocity, are stable.  For target patterns, we derive an
integro-differential equation that describes the evolution of a circular
excitation.  Its asymptotic behavior is handled exactly.  We illustrate
the analytic results by parallel-computer simulations of a network of
10^6 neurons. In so doing, we exhibit a novel type of local excitation,
a so-called `paternoster'. 


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Werner Kistler   Phone: +49(89)289.12193
Dipl.-Phys.      Fax:   +49(89)289.12296
                 email: wkistler at physik.tu-muenchen.de
                 WWW:   http://www.physik.tu-muenchen.de/~wkistler

Institut f"ur Theoretische Physik
Physik-Department der Technischen Universit"at M"unchen
James-Franck-Strasse
D-85748 Garching bei M"unchen
Germany
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